A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

A block is moving on an inclined plane making an angle $$45^\circ $$ with the horizontal and the coefficient of friction is $$\mu $$. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 $$\mu $$, then N is

Four solid spheres each of diameter $$\sqrt 5 $$ cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4 cm. The moment of inertia of the system about the diagonal of the square is N $$ \times $$ 10⁻⁴ kg-m², then N is

5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is